FINITE-TEMPERATURE REAL-ENERGY-AXIS SOLUTIONS OF THE ISOTROPIC ELIASHBERG INTEGRAL-EQUATIONS

A fast, efficient algorithm has been developed for calculating the fin ite-temperature real-energy-axis solutions of the Eliashberg integral equations for an arbitrary form of the electron-boson coupling functio n and Coulomb repulsion. Using this algorithm, the complex superconduc ting gap function Delta(omega,T), and the complex renormalization func tion Z(omega,T), have been obtained for a variety of forms of the elec tron-boson coupling spectrum. In addition, by calculating Delta(omega, T) at finite temperatures, the superconducting critical temperature T- c has been obtained for a variety of model systems. These results comp are well with the approximate analytic expression derived by Alien and Dynes for values of lambda less than 0.75. The solution of the Eliash berg equations has also been obtained for a model in which there are t wo well separated peaks in the electron-phonon coupling spectrum. This form of coupling spectrum is found to be particularly effective in ra ising the T-c of the model system. Further, this model has been extend ed and the solution of the Eliashberg equations has been obtained with an electron-boson coupling spectrum consisting of both an electron-ph onon component and a high-energy electronic electron-boson component. This form of the electron-boson coupling function may have special sig nificance in the field of high-temperature superconductivity.